To solve the inequality \( s^3 \geq 3 \), we start by isolating \( s \).
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Take the cube root of both sides: \[ s \geq \sqrt[3]{3} \]
Since the cube root function is increasing, there are no sign changes needed when taking the cube root.
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Identify the solution: The solution to the inequality is \( s \) such that: \[ s \geq \sqrt[3]{3} \]
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Graph the solution:
- The endpoint \( s = \sqrt[3]{3} \) is included in the solution, so we will use a closed dot.
- The solution extends to positive infinity.
- We represent this graphically as a line starting at \( \sqrt[3]{3} \) (closed dot) and extending to the right.
Here’s a description of the graphing actions:
- Plot \( \sqrt[3]{3} \) on the number line with a closed endpoint (●).
- Draw a line extending to the right of this point indicating all values greater than \( \sqrt[3]{3} \).
If you want to change the endpoint from closed to open for any reason, you could consider what happens if the inequality were strict (\( s^3 > 3 \)), but since here we are working with \( s^3 \geq 3 \), we keep it closed as stated above.
Thus, the final solution can be represented on a number line as follows:
\[ \text{Graph:} \]
<---|--------|--------|--------|--------|--------|--------|--------|--->
-2 -1 0 1 2 sqrt[3]{3} 3 4
●====================>
Here, the filled dot at \( \sqrt[3]{3} \) indicates that \( \sqrt[3]{3} \) is included in the solution, and the right-pointing arrow indicates that the solution goes to positive infinity.